For two-community geometric hidden community models, exact recovery is achievable above the Chernoff-Hellinger threshold even without the distinctness-of-distributions assumption, via a two-phase linear-time algorithm.
The geometric block model
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Sharp exact recovery threshold for two-community Euclidean random graphs
For two-community geometric hidden community models, exact recovery is achievable above the Chernoff-Hellinger threshold even without the distinctness-of-distributions assumption, via a two-phase linear-time algorithm.